In this paper we consider various multi-component splittings based on the trapezoidal rule and the implicit midpoint rule. It will be shown that an important requirement on such methods is internal stability. The methods will be applied to initial-boundary value problems. Along with a theoretical analysis, some numerical test results will be presented.<\/p>","DOI":"10.1090\/s0025-5718-98-00984-3","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:14:44Z","timestamp":1027721684000},"page":"1047-1062","source":"Crossref","is-referenced-by-count":19,"title":["Trapezoidal and midpoint splittings for initial-boundary value problems"],"prefix":"10.1090","volume":"67","author":[{"given":"Willem","family":"Hundsdorfer","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/0021-9991(76)90110-8","article-title":"An implicit finite-difference algorithm for hyperbolic systems in conservation-law form","volume":"22","author":"Beam, Richard M.","year":"1976","journal-title":"J. Comput. 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CWI Report, 1996."},{"issue":"187","key":"8","doi-asserted-by":"publisher","first-page":"81","DOI":"10.2307\/2008350","article-title":"Stability and convergence of the Peaceman-Rachford ADI method for initial-boundary value problems","volume":"53","author":"Hundsdorfer, W. H.","year":"1989","journal-title":"Math. Comp.","ISSN":"http:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"4","key":"9","doi-asserted-by":"publisher","first-page":"652","DOI":"10.1007\/BF01936143","article-title":"\ud835\udc35-convergence of the implicit midpoint rule and the trapezoidal rule","volume":"25","author":"Kraaijevanger, J. F. B. M.","year":"1985","journal-title":"BIT","ISSN":"http:\/\/id.crossref.org\/issn\/0006-3835","issn-type":"print"},{"key":"10","unstructured":"R.J. LeVeque, Intermediate boundary conditions for LOD, ADI and approximate factorization methods. ICASE Report 85-21, Langley Research Center, 1985."},{"issue":"1-3","key":"11","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/0168-9274(95)00056-Z","article-title":"Interior estimates for time discretizations of parabolic equations","volume":"18","author":"Lubich, Christian","year":"1995","journal-title":"Appl. Numer. Math.","ISSN":"http:\/\/id.crossref.org\/issn\/0168-9274","issn-type":"print"},{"key":"12","doi-asserted-by":"crossref","unstructured":"G.I. Marchuk, Splitting and alternating direction methods. Handbook of Numerical Analysis 1 (P.G. Ciarlet. J.L. 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